If \((U,w)\)  is a strong solution of (REF ), then \(U \in D({\mathbb {A}})\) , which, in turn, implies that \(u = U + W_A \in D({\mathbb {A}})\) , and hence \((u,w)\)  is a strong solution of (REF ). Since \(S_A(t)\)  is an analytic semigroup, the Theorem 5.14 [1]} for \(\alpha \in (0,1/2)\) , the process \(W_A(\cdot )\)  has \(\alpha \) -Holder continuous trajectories in \(H = L^2(D)\) . Following [2]}, introduce
\(Z:=H \times B, \ B = L^{\infty }(D)\) 
